Welfare in the volunteer’s dilemma

Abstract

We study the volunteer’s dilemma with heterogeneous costs and private information. We characterize efficiency properties of equilibrium. While the probability of success – the focus of previous theoretical analysis – may be strictly decreasing in group size, per-capita welfare is always increasing for every possible cost, strictly for sufficiently high costs. As group size increases, the expected utility of every member, regardless of their cost, converges to the expected utility of a member with the lowest possible cost, which is the same expected utility when there is no free rider problem, i.e., with only a single player in the game who has the lowest possible cost. Convergence, however, is slower than the convergence to zero of $1/n$, so the total inefficiency diverges at infinity, even if the lowest cost is zero.